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The error model of the initial alignment of the marine strapdown inertial navigation system is nonlinear, while the azimuth angle error is large on the swaying base. For this nonlinear model, a new nonlinear filter called as the central difference Gaussian Particle filter is proposed, which is based on the central difference Kalman filter and the Gaussian Particle filter. The central difference Kalman filter is used to calculate the estimate value and the covariance matrix in the observation update for the distribution function, which is sampled as the importance density function for the Gaussian Particle filter. The simulation results demonstrate the novel filter has better estimation performance than the unscented Kalman filter and the Gaussian Particle filter for the initial alignment.